Properties

Label 280.2.q
Level $280$
Weight $2$
Character orbit 280.q
Rep. character $\chi_{280}(81,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $5$
Sturm bound $96$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
Sturm bound: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(280, [\chi])\).

Total New Old
Modular forms 112 16 96
Cusp forms 80 16 64
Eisenstein series 32 0 32

Trace form

\( 16q + 4q^{3} - 2q^{5} + 4q^{7} - 6q^{9} + O(q^{10}) \) \( 16q + 4q^{3} - 2q^{5} + 4q^{7} - 6q^{9} + 2q^{11} + 16q^{13} - 4q^{17} - 2q^{19} - 6q^{21} - 8q^{25} - 32q^{27} + 4q^{29} - 16q^{31} - 2q^{35} + 4q^{37} + 20q^{39} + 8q^{41} + 48q^{43} - 12q^{45} + 12q^{47} - 2q^{49} + 4q^{51} - 4q^{53} + 8q^{57} - 4q^{59} + 2q^{61} - 12q^{63} - 6q^{65} - 12q^{67} + 4q^{69} - 48q^{71} - 12q^{73} + 4q^{75} - 48q^{77} - 8q^{79} - 16q^{81} - 88q^{83} - 44q^{87} + 14q^{89} + 12q^{91} - 44q^{93} - 4q^{95} - 16q^{97} + 92q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(280, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
280.2.q.a \(2\) \(2.236\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(-5\) \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
280.2.q.b \(2\) \(2.236\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(1\) \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
280.2.q.c \(2\) \(2.236\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(1\) \(4\) \(q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
280.2.q.d \(4\) \(2.236\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(-2\) \(-2\) \(q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
280.2.q.e \(6\) \(2.236\) 6.0.11337408.1 None \(0\) \(0\) \(-3\) \(6\) \(q-\beta _{5}q^{3}+(-1+\beta _{2})q^{5}+(1-\beta _{1}-\beta _{5})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(280, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)